Measurement method for a surface-measuring measuring machine

ABSTRACT

Measurement method where a code projection which is dependent on a three-dimensional position of a code carrier relative to a sensor arrangement is generated on a sensor arrangement, and at least part of the code projection is captured. An angular position of the code carrier with reference to the defined axis of rotation is ascertained and a current measurement position of the measurement component relative to a base is determined, wherein, a position value for at least one further degree of freedom of the code carrier relative to the sensor arrangement is ascertained on the basis of the code projection and is taken into account to determine the current measurement position, and a relative position of the connecting element with respect to the holder and/or the deformation thereof is determined from the position value in the form of a change in shape or size.

FIELD OF THE INVENTION

The invention relates to a measurement method for a surface-measuringmeasuring machine, a connection arrangement, in particular a tilting orrotary connection, for a measuring machine, and a coordinate measuringmachine comprising an articulated arm.

BACKGROUND

Measurement methods and measuring machines, such as, for example,coordinate measuring apparatuses or machines, e.g. comprising anarticulated arm, have been known for a long time. By way of example,these apparatuses are used for the measurement of object surfaces whichis carried out with high accuracy, in particular in the manufacturingindustry, for which the measurement and testing of workpiece surfacesare of great importance.

3D coordinate measuring articulated arms of the generic type aredescribed in U.S. Pat. No. 5,402,582 or EP 1 474 650, for example.Comparable systems, also called “articulated arm” or “portable CMM”, areoffered e.g. by the company “Romer” with the product names “Sigma”,“Flex” or “Omega” and the company “CimCore” with the product names“Infinite” or “Stinger”.

3D coordinate measuring articulated arms have a base, which ispositioned fixedly and in a known manner in a reference coordinatesystem, as one end of the articulated arm and an opposite movablemeasurement end, on which a measurement component or a measurement probeis arranged. A tactile probe can be used as a standard probe, whichtactile probe can be brought into contact with a measurement point of anobject surface and consists, for example, of a ruby sphere mounted on ameasurement rod.

As an alternative thereto, optical sensors are also known as measurementcomponents, which optical sensors can be embodied for example as pointmeasuring devices or as scanners, i.e. as scanning an object surfacecontinuously and e.g. line by line. More specifically, triangulationsensors or interferometric measurement arrangements can be used as suchoptical sensors. Furthermore, European Patent Application No.07124101.2, for example, describes the use of a camera as measurementcomponent which is designed for capturing or detecting a measurementobject surface and is mounted on the movable end of an articulated arm.On the basis of the articulated arm coordinate measuring machine, it ispossible to determine highly precisely a position and orientation of thecamera in spatial terms.

Arranged between the two ends of the articulated arm there are aplurality of members or arm sections which are connected pivotablyand/or rotatably with respect to one another and, if appropriate,displaceably with respect to one another, such that the measurement endwith the measurement component, which is also designated as sensingmember, is freely movable within a spatial section. For this purpose,the members of the arm are connected to one another by means ofarticulated joints and, if appropriate, by means of suspensions, whichenable a linear displacement. Furthermore, position measuring devicesare assigned to the articulated joints and/or suspensions, such that ineach case a position or orientation of the members with respect to oneanother, that is to say a relative position in each case between themembers, can be measured. By way of example, angle measuring devicesand/or length measuring devices that determine lengths, rotationalangles or pivoting angles as measurement variables are used for thispurpose.

From the knowledge of an instantaneous measurement position of themembers, i.e. of the respective relative positions of the members withrespect to one another and of one of the members with respect to thebase, it is possible to determine the orientation of the individual armelements and of the measurement component relative to the base in areference coordinate system. The position of the measurement componentis generally determined by an evaluation unit to which these measurementvariables measured by the respective position measuring devices arecommunicated and which derives the position of the measurement componenttherefrom. For example, computers or computing units specificallyprogrammed for this application can be used for this purpose. By meansof the reference—which can be ensured by means of the base—to theexternal reference coordinate system, it is possible to determine notonly the orientation but also the position of the arm elements and ofthe measurement component, i.e. location and orientation in spatialterms.

In accordance with the generic type, the rotary articulated joints of anarticulated arm are assigned in each case optoelectronic angle measuringdevices that are used to determine in each case a relative rotationalposition of the two members connected by means of the articulated joint.The articulated joint generally consists of the two arm membersconnected rotatably to one another, between which a rotary encoder orangle measuring device is arranged. In this case, the optoelectronicangle measuring device or rotary encoder serves for measuring aninstantaneous relative rotational position of its rotary bearingcomponents with respect to one another, and thus indirectly of the twoarm members. For this purpose, it has a code carrier or a code element,which is arranged on one of the two arm members, and a sensorarrangement, which is correspondingly fitted to the other arm member.

In this case, the code carrier is then mounted in the rotary articulatedjoint in such a way as to enable a relative rotational movement of thecode carrier relative to the sensor arrangement about an axis ofrotation. The element of the second articulated arm member that isrotatable with respect to the receptacle of a first arm member, thesensor arrangement and also the code carrier mounted rotatably thereinwith respect to one another of the sensor arrangement can in this casebe designated as rotary bearing components.

In the case of such optoelectronic embodiments, pattern elements as codeof the code carrier are optically imaged onto the sensor arrangementcomposed of one or a plurality of read heads, e.g. CCD or CMOS line orarea sensors, as disclosed in CH 658514, for example. From the positionof the code projection, in particular the projected pattern elements, onthe sensor arrangement or the read heads thereof, it is possible todeduce the relative rotational angle of the code carrier as rotary bodywith respect to the sensor arrangement. In this case, a detector centerserves as reference variable, wherein ideally both detector center, thepivot point, and the center of the pattern elements lie on the axis ofrotation, without mechanical eccentricity errors.

By means of such methods and apparatuses, with corresponding precautionsit is even possible, with a measurement accuracy of the order ofmagnitude of a few angular seconds, to resolve a complete circle intomore than one million units.

In order to be able to achieve such high accuracies, firstly the sensorarrangement has to be arranged positionally stably with respect to thebearing. Secondly, a high dimensional and shape stability of the codecarrier, in particular the arrangement and embodiment of the codeelement on the code carrier—with pattern elements arranged around apattern center one behind another in the direction of rotation—is anecessary prerequisite. Besides partial graduation inaccuraciesattributable to deviations of the predefined distances betweenindividual pattern elements arranged one behind another and/or todeviations of the dimensions of the pattern elements themselves, inpractice a spacing-apart of the pattern center from the axis ofrotation, a so-called eccentricity, often makes it impossible to achieverequired accuracies. On account of manufacturing tolerances that can beavoided only with difficulty and in practice always exist, each codecarrier has an eccentricity. Radial runouts of the bearing or a bearingplay can additionally make a contribution to the eccentricity. Ifappreciable loads owing to forces act on the rotary articulated jointsof the articulated arm during the determination of the sensing positionor the rotational angles, then permanent or temporary eccentricities andother changes in position of the code carrier with respect to thereceptacle of the rotary articulated joint can likewise occur dependingon the loads.

Methods and apparatuses for determining the rotational angle andcalibrating out such undesirable changes in position with respect to theideal position, for example owing to loads on the rotary articulatedjoint or owing to bearing faults and/or radial runouts, are described,inter alia, in European Patent Application No. 07100296.8 and thepublications EP 1,632,754 A1, U.S. Pat. No. 7,051,450 B2 and U.S. Pat.No. 7,069,664 B2.

In this case, EP 1,632,754 A1 discloses a method for measuring thecurrent eccentricity of a rotary encoder, wherein at least some of amultiplicity of pattern elements arranged around a pattern center areimaged by means of optical beams on an optical detector. The patternelements are arranged on a code carrier, which is connected to thedetector in a manner rotatable about the axis of rotation. Positions ofthe imaged pattern elements are resolved by means of the detectorelements of one and the same detector. In a first step, effects of aneccentricity of the pattern center with respect to the axis on thedetermination of a rotational angle are determined computationally bymeans of resolved positions of at least one pattern element. In a secondstep, taking into account the effects determined, the rotational angleis determined accurately by means of the resolved positions of patternelements arranged one behind another.

In a development of this method, in the first step, by means of anintermediate step, pattern elements arranged one behind another arecombined to form at least two groups and at least two group positionsare determined computationally by means of the resolved individualpositions of the respectively combined pattern elements. Effects of theeccentricity on the determination of the rotational angle are thendetermined computationally by means of the at least two group positionsdetermined. By means of the group positions determined, this can beeffected with higher accuracy.

The International Patent Application WO 2008/083797 describes, for thepurpose of determining an eccentricity error for a rotational angleabout an axis on the basis of resolved positions of pattern elementsprojected onto a sensor arrangement, in a first step, for a multiplicityof measurements, computationally determining the eccentricity of thepattern center with respect to the detector center. In a second step, bymeans of aggregation, i.e. by means of combination and linkage, from themultiplicity of measured values at least one influencing variable can beseparated or determined. Depending on the approach, the influencingvariables are either determined or else suppressed, e.g. by averagingout. Influencing variables determined can then be used eitheralgorithmically or else for direct correction of the eccentricity, e.g.for mechanical correction of the axial position by means of actuatingelements or electronically by adaptation.

Furthermore, it is explained therein that—besides the influencingvariables which lead to a direct eccentricity contribution in the planeof the sensor arrangement, such as e.g. the translational displacementof the bearing shaft—the movement in the direction of the axis ofrotation can also be determined by means of suitable angle measuringheads. As a result of the change in distance of the code element withrespect to the sensor arrangement, the projection scale of the codechanges. This change in projection scale can be used as a measure of thechange in distance or the position in an axial direction. If thedistances with respect to the code disk as code element are determinedfor two detector elements, then the tilting of the axis can also bedetermined.

U.S. Pat. No. 7,051,450 B2 and U.S. Pat. No. 7,069,664 B2 describe acoordinate measuring machine (CMM) comprising an articulated arm havinga plurality of rotary articulated joints between a base of the arm and ameasurement component arranged on the other arm end. For measuring ameasurement position of the measurement component, the rotaryarticulated joints are in each case assigned angle measuring devicescomprising a sensor arrangement composed of at least two read heads anda code element arranged rotatably with respect to the two.

It is demonstrated in this case that the at least two read headscooperate with one another in such a way as to reduce an error caused byloads of the rotary articulated joint during the rotational anglemeasurement.

By way of example, two read heads offset by 180° in a circumferentialdirection, three read heads offset by 120° in each case in acircumferential direction, or alternatively four read heads offset by90° in each case in a circumferential direction are provided for thispurpose.

As already indicated above, therefore, these methods and apparatuses inthe prior art always provide for taking into account, eliminating,calibrating out or compensating for errors which influence the anglemeasurement, exclusively for the determination of the rotational angle.Errors taken into account include e.g. wobble errors owing to aninclination of the rotation axis, eccentricity errors owing tomanufacturing tolerances or a bearing play, and further errors, causedfor example by loads of the rotary articulated joint. A dedicateddetermination and quantification of the influencing variables and thefurther processing thereof outside the rotary encoder do not take place.

However, in the case of coordinate measuring machines comprising anarticulated arm having rotary articulated joints, owing to the describederror influences such as loads of the rotary articulated joints—over andabove an erroneous determination of the angular position—further errorsarise in the context of determining the measurement position of themeasurement component.

Specifically, in practice—over and above the rotation actually providedby the rotary articulated joint—further changes in position of the codecarrier with respect to the receptacle occur, in particular axialdisplacements, radial displacements or tiltings, which can have variouscauses. Although they are minimal changes in position, thesenevertheless lead to appreciable errors given the accuracies required inthe meantime for the position determination.

SUMMARY

Therefore, one object of the invention is to provide an improvedmeasurement method for a surface-measuring measuring machine, inparticular for a coordinate measuring machine comprising an articulatedarm having rotary or tilting articulated joints, for determining themeasurement position of a measurement component.

A further object is to provide an improved coordinate measuring machinecomprising an articulated arm having rotary articulated joints asconnection arrangements.

In particular, in this case, with little hardware modification outlay onthe part of the articulated arm, the intention is to make it possible todetermine the measurement component measurement position with higheraccuracy.

The measurement method according to the invention for asurface-measuring measuring machine, e.g. for a coordinate measuringmachine comprising an articulated arm having rotary articulated jointsfor determining a measurement position of a measurement component,breaks away from methods in the prior art, in which it is always thecase that only in the context of determining an angular position of therotary or tilting articulated joint is provision made for taking intoaccount or compensating for error influences—such as e.g. load-governeddisplacements or tilting of the axis of rotation, wherein the armmembers as connection elements from the base to the measurementcomponent are regarded as influenced.

By contrast, according to the invention, such changes in position of thecode carrier, mounted rotatably in a receptacle, of a rotary articulatedjoint with respect to the assigned sensor arrangement are explicitlydetermined and used as additional measurement variables, which describethe measurement position of the arm members of the articulated arm, forderiving the measurement position of the measurement component relativeto a base. This means that a change in position of the two arm membersconnected by means of the rotary articulated joint—which change inposition is caused by loads, for example, in the rotary or tiltingarticulated joint as connection arrangement and goes beyond a change inrotational position—is determined in terms of its extent and is takeninto account when determining the relative position of the two armmembers with respect to one another. Deformations or changes in size ofcomponents can likewise be deduced from these position values accordingto the invention.

The determination of the changes in position such as

-   -   a displacement of the code carrier with respect to the sensor        arrangement in a radial direction relative to the axis of        rotation,    -   a displacement of the code carrier with respect to the sensor        arrangement in the direction of the axis of rotation and/or    -   a tilting of the code carrier with respect to the receptacle,

or of position change magnitudes associated with said changes inposition is effected on the basis of an optoelectronic positionmeasuring device between the code carrier and the sensor arrangement, inparticular on the basis of an optoelectronic angle measuring devicealready assigned to the rotary articulated joint anyway.

For this purpose, the position measuring device has a code, which isapplied to one of the rotary articulated joint components—namelydirectly or via a dedicated component, and a sensor arrangement composedof at least one read head. In this case, the sensor arrangement isarranged on the respective other rotary articulated joint component anddetects a code projection generated on the basis of the code carrier. Inthis case, code projection should be understood to mean a projection ofat least part of an optically detectable code possessed by the codeelement. In particular, the code carrier used can be a dedicated codedisk connected to one of the articulated arm members. Alternatively,however, the code can also be situated directly on one of the armmembers, such that this serves structurally as a code carrier.

Code carriers and sensor arrangements of the generic type, wherein thedescribed changes in position of the code relative to the sensorarrangement can be determined on the basis of a read code projection,are sufficiently known from the prior art. However, these changes inposition, in accordance with apparatuses and methods in the prior art,are used only for calibration and thus improvement of an anglemeasurement. In this case, however, the displacements or tilting derivedfrom the code projection are not used for describing thethree-dimensional relative position of the components of the rotaryarticulated joint with respect to one another. Consequently, in thecontext of previous measurement position determinations in the case ofarticulated arms the idealistic assumption that the rotary articulatedjoint allows exclusively a relative rotational movement of the rotaryarticulated joint components with respect to one another—that is to saya movement with one degree of freedom—is always taken as a basis.

According to the invention, now for the rotary encoder, on the basis ofthe code projection, a position value for at least one further degree offreedom of the code carrier relative to the sensor arrangement assignedthereto is determined and taken into account when determining thecurrent measurement position of the measurement component or of theprobe, wherein the position value is used to determine a relativeposition of the connection element with respect to the receptacleconnected thereto or the deformation thereof. This means that, accordingto the invention, the changes in position of the code carrier which gobeyond the rotation are related to the position or orientation and apossible deformation of a connection element of the measuring machine,e.g. of an arm element.

In this case, the determination of the measurement position can both bebased also model-based approaches, in which the geometrical andmaterial-dependent variables of the connection elements, such as e.g.their length and inherent weight or an external weight having an effect,are taken into account, and it is also possible to use a solution basedon calibrations, in which solution known positions and orientations areassigned corresponding position values, which, for their part, can againsupply a basis for a descriptive function or else can also be stored inlook-up tables. By their nature these approaches can also be combined,however, e.g. by additional calibrations being effected in selectedmeasurement positions on the basis of a modeling. Moreover, variablesdetermined by other sensors, such as e.g. temperature sensors, can alsobe used supplementarily in the model.

By virtue of the use according to the invention of the determinedchanges in position for describing the exact relative position of therotary encoder or connection arrangement components with respect to oneanother and thus as further measurement variables which specifying therelative position of the articulated arm members and are taken intoaccount when calculating the measurement position of the probe relativeto the base, with little hardware modification outlay on the part of thearticulated arm it becomes possible to determine the measurementcomponent measurement position with higher accuracy.

By way of example, according to the invention, an occurring tilting ofthe code carrier of a rotary articulated joint about the actual rotationaxis is detected in terms of its extent and is taken into accountdirectly as current relative measurement position of the membersconnected by means of the rotary articulated joint and is thus includedin the determination of the measurement position of the probe.

In model-based approaches, depending on the embodiment of the connectionelement, the latter can be regarded as rigid or else as deformablewithin limits. Accordingly, any change can be regarded as occurring onlyin the articulated joint or the connection arrangement or else a changein the components is also considered. It is thus possible to model thefact that, depending on the arrangement of rotary encoder axis and axisof the connection element and with knowledge of the inherent weight ofthe connection element and depending on the orientation of adjacentconnection elements or arm members, division into position-governed anddeformation-governed portions is also effected. Thus, in the case of thefitting of the rotary encoder on the longitudinal axis of the connectionelement and the perpendicular position thereof, the flexure and thusdeformation and also load-governed tilting of the code carrier withrespect to the sensor arrangement are minimal, wherein oppositelongitudinal displacements, i.e. translations in an axial direction,occur in a suspended and in a standing position of the arm member. Thus,deformations of the individual components of a measuring machine canalso be identified and determined in terms of their effect.

Particularly in the case of exchangeable measurement components, byvirtue of the different weights thereof, the connection arrangements canalso be influenced in a correspondingly deviating manner, whichinfluencing can be determined by the offset according to the invention.

In this case, it should also be taken into consideration that, in thecase of the high-precision applications required here, thermallygoverned changes, such as e.g. length or radius changes, already causeeffects on the measurement position, which effects can likewise be takeninto consideration or identified by the approach according to theinvention.

The sensor arrangement of the position measuring device can consist, inparticular, of at least two read heads. By way of example, as sensorarrangement, two read heads are arranged in a manner offset by 90° in acircumferential direction or, alternatively, three read heads arearranged with an offset of 60° in each case. The read heads can in thiscase be embodied in a known manner e.g. as line sensors having amultiplicity of detector elements strung together.

As code element or code carrier it is possible to use, in particular, acode disk having an optically readable code, e.g. in the transmittedlight method. In this case, the code can have a multiplicity of patternelements arranged one behind another in a circumferential direction,wherein the totality of the pattern elements can represent both anincremental and an absolute code. Alternatively, however, the code canalso be situated on a different carrier, e.g. on the end face of housingcomponents, which can then be illuminated e.g. in the reflected lightmethod.

Preferably, according to the invention, an optoelectronic rotary encodersuch as is already present anyway in some rotary articulated joints ofarticulated arms from the prior art can be used as the positionmeasuring device. In particular, however, also for the rotaryarticulated joint—in addition to the angle encoder embodied according tothe prior art and assigned to the rotary articulated joint—a furtherrotary encoder or some other functionally similar form of thecombination of code carrier and sensor arrangement can be provided as anoptoelectronic position measuring device, wherein the latter servesspecifically for detecting the changes in position of the code carrierrelative to the sensor arrangement.

As already described above, in this case the following changes inposition of the code carrier relative to the receptacle—and thus of afirst arm member, representing the code carrier, relative to a secondarm member, having the receptacle—are determined and taken into accountwhen deriving the exact relative position of the members with respect toone another:

-   -   a displacement of the code carrier with respect to the sensor        arrangement in a—with respect to the axis of rotation—radial        direction,    -   a displacement of the code carrier with respect to the sensor        arrangement in a—with respect to the axis of rotation—axial        direction and/or    -   a tilting of the code carrier relative to the sensor        arrangement.

As position change variables linked therewith it is possible todetermine for example

-   -   a radial displacement direction (RR) and a radial displacement        extent (Δr),    -   an axial displacement extent (Δh) and    -   a tilting direction and a tilting angle (Δκ).

The position change variables—alongside the further arm positionmeasurement variables designating the measurement position of the armmembers—are related to one another, from which the measurement positionof the measurement component relative to the base is derived.

For this purpose, the coordinate measuring machine designed according tothe invention has an evaluation unit, by means of which the arm positionmeasurement variables detected by individual member position measuringdevices—also including according to the invention the position changevariables with respect to the at least one rotary articulated joint—arelinked with one another and the measurement position of the measurementcomponent is derived therefrom.

BRIEF DESCRIPTION OF THE DRAWINGS

The measurement method according to the invention and the connectionarrangement according to the invention and a coordinate measuringmachine according to the invention are described in greater detailpurely by way of example below on the basis of concrete exemplaryembodiments illustrated schematically in the drawings, furtheradvantages of the invention also being discussed. In the figures,specifically:

FIG. 1 shows a generic coordinate measuring machine with articulated armhaving rotary and/or tilting articulated joints;

FIG. 2 shows a connection arrangement according to the invention of anarticulated arm;

FIG. 3 shows the connection arrangement according to the invention fromFIG. 4 with an illustrated axial displacement of the code carrier;

FIG. 4 shows the connection arrangement according to the invention fromFIG. 4 with an illustrated radial displacement of the code carrier;

FIG. 5 shows the connection arrangement according to the invention fromFIG. 4 with an illustrated tilting of the code carrier;

FIG. 6 shows the connection arrangement according to the invention fromFIG. 4 with a tilting of the code carrier and with a flexure of the armmembers;

FIG. 7 shows the connection arrangement according to the invention witha further embodiment for a rotary encoder assigned thereto;

FIG. 8 shows a code projection onto a sensor arrangement, which codeprojection is suitable for reading displacements and/or tilting of thecode carrier with respect to the receptacle;

FIG. 9 shows a code projection suitable for reading displacements and/ortilting of the code carrier with respect to the sensor arrangement; and

FIG. 10 shows a further code projection suitable for readingdisplacements and/or tilting of the code carrier with respect to thesensor arrangement.

DETAILED DESCRIPTION

FIG. 1 shows purely by way of example a generic coordinate measuringmachine 1 with articulated arm for determining the position of ameasurement point as an example of a measuring machine for surfacemeasurement. In this case, the coordinate measuring machine 1 has a base4—which is positioned fixedly and in a known manner in a referencecoordinate system. Proceeding from the base, successively by way ofexample seven arm members 5 a-5 g as connection elements are connectedto one another via articulated joints enabling relative rotationalmovements and/or via suspensions enabling relative linear movements. Forillustration reasons, i.e. for more comprehensible illustration, thesearticulated joints and suspensions are not shown explicitly visibly inFIG. 1 , but generic articulated joints and suspensions are sufficientlyknown to the person skilled in the art anyway.

In this case, a first of the members 5 a is fixed to the base 4 movablyrelative thereto, a second of the members 5 b is fixed to the firstmember 5 a movably relative thereto, etc. The seventh member 5 g has ameasurement component 6 and forms overall as structural element thesensing member TG. The measurement component 6 is thus freely movablewithin a spatial section and can e.g. be brought to a measurementposition manually by a user, wherein the mechanical contact with base 4is ensured by the sequence of connection elements. By way of example,the probe 6 is embodied as a ruby sphere for making contact with a pointto be measured of an object surface, but contactlessly measuring systemscan also be arranged and used in the same way. Alternatively, however,further measurement components known from the prior art can also be usedinstead of the tactile probe. Thus, by way of example, opticalsensors—in particular an optical distance measuring device, e.g.interferometric measuring arrangements, a laser scanner or a camera forscanning the surface—can be used as measurement component.

By way of example, the coordinates of a reference point of themeasurement component 6 and, in particular, additionally a currentorientation of the measurement component 6 in the respective currentmeasurement position are specified as measurement position.

In this case, for simpler differentiation, the members 5 a-5 g areillustrated with respectively alternately different hatching in FIG. 1 .Base 4 and sensing member TG are shown without hatching.

A plurality of position measuring devices 8 a-8 f for measuringpositions of the members 5 a-5 g in each case with respect to oneanother are assigned in each case to the articulated joints and/orsuspensions. By way of example, as the position measuring devices 8 a-8f, optoelectronic rotary encoders are provided as position measuringdevices 8 a, 8 c, 8 d, 8 f and length measuring devices are provided asposition measuring devices 8 b, 8 e, which are designed for measuringarm position measurement variables α, β, γ, δ, ε, a, b, c linked withthe relative position of the members. Consequently, angles α, β, γ, δ, εand length deflections a, b, c between the members 5 a-5 g are thereforein each case measured as arm position measurement variables α, β, γ, δ,ε, a, b, c.

In this case, an evaluation unit 7 is designed for receiving the armposition measurement variables α, β, γ, δ, ε, a, b, c determined for ameasurement position. On the basis of these arm position measurementvariables α, β, γ, δ, ε, a, b, c indicating the relative positions ineach case of the arm members with respect to one another, the evaluationunit derives the measurement position or the coordinates of themeasurement component 6 and displays said position or said coordinatese.g. on a display.

FIG. 2 shows a connection arrangement according to the invention, e.g.of an articulated arm, for use with a measurement method according tothe invention, wherein the connection arrangement has a rotary encoder9, which detects the rotation of the at least one connection element 10,e.g. a first arm member, with respect to a receptacle 11, e.g. as end ofa second arm member. In this case, the measurement component isconnected to the base indirectly by a sequence of connection elements10, but according to the invention it is also possible to realizemeasuring machines with only a single connection element 10 and thus adirect connection of the measurement component to the base by this oneconnection element 10.

The rotary encoder 9 comprises in each case a code carrier 12 and asensor arrangement 13, wherein code carrier 12 and sensor arrangement 13are rotatable with respect to one another about a defined axis ofrotation DA as a first degree of freedom. For this purpose, a codeprojection dependent on the three-dimensional position of the codecarrier 12 relative to the sensor arrangement 13 is produced on thesensor arrangement 13 and at least part of the code projection isdetected by said sensor arrangement. In this case, the rotary encoder 9is constructed in a manner known per se from a code carrier 12 rigidlyconnected to the receptacle 11 and having an optically detectable code,which can be embodied, for example, as a code-carrying glass or plasticdisk, and the sensor arrangement 13 consisting of one or more detectorelements and serving for detecting the code projection, which can becorrespondingly fitted in the connection element 10. For this purpose,the sensor arrangement 13 can have, for example, two read headsrespectively having a line arrangement of optical detector elements. InFIGS. 2 to 6 , the sensor arrangement 13 arranged in the connectionelement 10 consists, for example, of two read heads—e.g. such as areknown according to the prior art. The code carrier 12 is assigned ascode carrier with a code disk functioning as “measurement table” andhaving a code extending in a circumferential direction. In this case,the code can have a multiplicity of pattern elements arranged in amanner strung together, wherein the pattern elements are embodied—e.g.in triangular form—in such a way that the code projection is suitable,in particular, for the additional reading of changes in position in thenon-rotation direction. The arrangement of the sensor arrangement 13 inthe connection element 10 and the mechanically rigid connection of thecode carrier 12 to the receptacle 11 constitute merely one example. Inparticular, this arrangement can also be reversed, i.e. according to theinvention it is likewise possible to realize a mechanically rigidarrangement of the code carrier 12 in the connection element 10 and themechanically rigid connection of the sensor arrangement 13 to thereceptacle 11.

In addition to an angular position, according to the invention furtherpositions of the first arm member with respect to the second arm memberare taken into account when determining the relative measurementposition, wherein the code carrier 12 embodied as a code disk serves asa “measurement table”. That means that the three-dimensional position ofthe code disk relative to the sensor arrangement 13 is read, for examplefrom a shadow casting of the code disk, wherein the code disk functionslike a tabletop whose shadow produced on the floor by a ceiling light isdependent on its standpoint and its inclination relative to the floor.In this case, a modification of the hardware already present incoordinate measuring machines is necessary only to a limited extent.Thus, the position measuring device, in particular the rotary encoder 9,according to the invention now has to take account of the determineddisplacements and/or tilting of the code carrier in the non-rotationdirection, which have a distorting effect on the angle measurement, notonly rotary-encoder-internally during the angle determination, but asfurther measurement position variables in addition to the angularposition determined to a superordinate evaluation unit, which calculatesthe measurement position for example from all measurement positionvariables of all member position measuring devices present in thearticulated arm.

On the basis of the code projection, therefore, the rotational positionof the code carrier 12 relative to the defined axis of rotation DA isdetermined and the current measurement position of the measurementcomponent relative to the base is determined using this informationavailable for all connection elements. For the rotary encoder 9, incontrast to solutions in the prior art, on the basis of the codeprojection a position value for at least one further degree of freedomof the code carrier 12 relative to the sensor arrangement 13 is alsodetermined and taken into account when determining the currentmeasurement position, wherein the position value is used to determine arelative position—corresponding to the further degree of freedom of thecode carrier—of the connection element 10 with respect to the receptacle11 and/or the deformation of said connection element. Although the anglemeasuring devices used in the prior art in some instances likewisedetermine lateral displacement or changes in distance of the code withrespect to the detectors, they use this information only for increasingthe accuracy in the angle measurement, i.e. in determining therotational position. By contrast, according to the invention, theposition value for the further degree of freedom is used to drawconclusions therefrom with regard to the position or orientation of theconnection element 10 and, if appropriate, the forces acting or adeformation of the connection element 10, wherein position and/ororientation of the connection element correspond to the further degreeof freedom of the code carrier 12. An eccentricity of the code carrier12 is thus used to determine an eccentric position of the connectionelement 10 with respect to the receptacle 11, wherein deviations in thevalue of the variable describing the further degree of freedom canoccur, however, on account of faults or changes in the relativepositioning of code carrier 12 and connection element 10. Thus, in thecase of a tilting of the code carrier 12, a corresponding tilting of theconnection element 10 with respect to the receptacle 11 is deduced,wherein this tilting, e.g. on account of elastic influences, can alsoturn out to be larger or smaller than the value of the tilting of thecode carrier 12. The degree of freedom of a tilting and/or of therotation about the assigned tilting axis is taken into consideration inboth cases, however.

As is described for example in the prior art documents cited above, thecode projection can then be read and changes in position—caused byradial runout errors and loads of the rotary articulated joint—of thecode element or code carrier 12 relative to the sensor arrangement13—i.e. for example deviations of a code center from the axis ofrotation DA— can be derived therefrom. In contrast to the use—knownaccording to the prior art—of said changes in position of the codecarrier 12 with respect to the sensor arrangement 13 merely forcorrecting an angle position to be determined of these two componentswith respect to one another, according to the invention said changes inposition are taken into account as variables which indicates therelative position of connection element 10, e.g. in the case of anarticulated arm of the first with respect to the second arm member, andare used as measurement position variables when calculating the positionof the measurement component with respect to the base. Consequently,changes in position of the code carrier 12 with respect to the sensorarrangement 13 which go beyond an angle of rotation are also explicitlydetermined from the detected code projection and used for determiningthe measurement position. Although such displacements and tilting aresubstantially prevented by a corresponding, precise mounting of the codecarrier 12, even minimal displacements and/or tilting affect theaccuracy for determining the measurement position of the probe.Consequently, the changes in position, which, although undesirable inprinciple, cannot completely be avoided, are not only accepted butdetermined and used as information for describing the overall state ofthe mechanical system of the measuring machine. Consequently, firstlythe change between the components assigned to the receptacle and thus toone arm member and the components of the connection element as the otherarm member is determined, such that changes in the articulated joint orthe connection arrangement can be quantified and taken into account.Secondly, the forces acting can be deduced from the extent of the changeand the angular positions, such that weight-governed deformations ofcomponents or the connections thereof can be determined. Moreover,thermal or ageing-governed changes in the connection arrangement canalso be detected and taken into account.

According to the invention, for this purpose at least one, but inparticular all of the following changes in position or position valuesare determined:

-   -   a displacement in a radial direction relative to the axis of        rotation DA,    -   a displacement in the direction of the axis of rotation DA        and/or    -   a tilting about the axis of rotation DA.

In particular, it is possible to determine the position values from thesame code projection which also serves for reading the angular positionof the code element relative to the sensor arrangement. According to theinvention it is likewise possible for the position values determinedfurthermore also to be used for correction and/or calibration whendetermining the angular position.

FIGS. 3 to 6 show, by way of example, changes in position caused byloading of the rotary articulated joint in the non-rotation direction ofthe code carrier 12 with respect to the sensor arrangement 13.

In FIG. 3 , the code carrier 12 is displaced relative to the sensorarrangement 13 in the direction of the axis of rotation DA. Such achange in position can be derived from the code projection, e.g. from ascale change of the code projection detected by the sensor arrangement.The associated position change variable can subsequently be communicatedas axial displacement extent (Δh) with regard to this rotary articulatedjoint to the evaluation unit.

In FIG. 4 , the code carrier 12 is displaced relative to the sensorarrangement 13 and with respect to the axis of rotation DA in a radialdirection. Such a change in position can be derived from the codeprojection, e.g. on the basis of displacements of those positions of thepattern elements which are resolved by the sensor arrangement 13. Theassociated position change variables can subsequently be communicated asradial displacement direction (RR) and radial displacement extent (Δr)with regard to this rotary articulated joint to the evaluation unit.

In FIG. 5 , the code carrier 12 is tilted relative to the sensorarrangement 13 and with respect to the axis of rotation DA. Such achange in position can be derived from the code projection, e.g. from ascale ratio of the code projection detected by the first read head tothe code projection detected by the second read head. The associatedposition change variables can be communicated e.g. as tilting directionand tilting angle (Δκ) with regard to this rotary articulated joint tothe evaluation unit.

As is illustrated in FIG. 6 , it can happen that in addition to thetilting and, if appropriate, the pure weight-governed and slightdeformation, going beyond that a flexure or deformation of the two armmembers connected rotatably with respect to one another is also broughtabout, e.g. as a result of a higher loading on the rotary articulatedjoint. Such a loading can occur, for example, when particularly heavymeasurement components are used, if such exchangeability of probes isprovided. On the basis of empirical experiments and/or taking account ofmodels or deformation parameters of the first and/or second arm membercarried out calculations, flexures of the arm members can now bedetermined as further measurement position variables—depending on thetilting—and used for deriving the measurement position of themeasurement component in a coordinate system spanned with respect to themeasuring machine base.

In this case, it is assumed that an extent of the tilting determined canbe used as a measure of a flexure of the arm members connected via therotary articulated joint—by modeling and to a good approximation.

By way of example, for this purpose it is possible to establish afunction of the flexure of one of the arm members depending on thetilting about the axis of rotation, which function is derived on thebasis of deformation laws for solid bodies and/or defined by empiricalexperiments. One example of such a function is illustrated in FIG. 7 ,wherein an extent of the flexure δL of the corresponding armmember—purely schematically and in principle—is plotted against thetilting angle ρ determined. In this case, the function can be chosen insuch a way that, up to a tilting angle predefined by a bearing play inthe rotary articulated joint, the extent of the arm articulated jointflexure is set as equal to zero. In this tilting range, the forcesacting on the arm members are transmitted, by the usually very stiffbodies of the arm members, substantially completely to the articulatedjoints, where they bring about for the time being precisely the tiltingabout the axis of rotation as carried out in the context of the rotaryarticulated joint play. If the code carrier has reached a stop in therotary articulated joint as a result of a tilting, then a furtherexertion of force also brings about a deformation of the arm memberssubstantially in the form of a flexure. Depending on the embodiment ofthe connection element, however, in this case it is also possible tomodel the above-described position- and weight-dependent deformationthereof.

FIG. 8 illustrates an alternative embodiment according to the inventionfor a connection arrangement in the form of a rotary articulated jointhaving two rotary encoders 9 and 9′.

In this case, the rotary articulated joint is assigned a first rotaryencoder 9 and a second rotary encoder 9′, in which the two opticallydetectable code disks as first and second code carriers 12 and 12′ arearranged at a distance from one another on a common axis as axis ofrotation DA. The two code disks are respectively assigned a sensorarrangement 13 and 13′ composed of at least two read heads, wherein thesensor arrangements 13 and 13′ in each case detect a code elementprojection and are arranged opposite each other in the connectionelement 10.

Such an arrangement as angle measuring device and additionally as ameasuring instrument for axial and/or radial displacements and/ortilting of the code carrier makes it possible to determine highlyprecisely the exact three-dimensional position of the code carriers 12and 12′ with respect to the sensor arrangements 13 and 13′. This exactlydetermined position, which is detected on the basis of measurementposition variables such as an angle of rotation about the axis ofrotation, a radial displacement direction, a radial displacement extent,an axial displacement extent, a tilting direction and/or a tiltingangle, can indeed be related taking account of the rigid coupling of thecode carriers 12 and 12′ on the one hand, and of the sensor arrangements13 and 13′, on the other hand, with respect to one another. Thus,extension and change in length of the common axis or of the housing ofthe connection element can be identified and quantitatively determinedon the basis of the change in distance of the code carriers 12 and 12′relative to the respective sensor arrangements 13 and 13′. Likewise, inthe case of an axis assumed to be rigid and oppositely directed tiltingof code carrier 12, 12′ and sensor arrangements 13, 13′ in the rotaryencoders 9 and 9′, it is possible to deduce a flexure of the connectionelement 10. In the case of an equidirectional tilting, by contrast, itis possible to deduce a largely rigid behavior of the connection elementand the total movement thereof.

According to the invention, it is possible, in particular, tosubstantially or completely replace other sensors in measuring machines,e.g. pure length-measuring sensors, such that a complete and highlyprecise determination of the measurement position or spatial position ofthe measurement component becomes possible solely by the use ofuniformly constructed rotary encoders. By virtue of the fact that thismakes it possible to exclusively use a single type of sensor, themechanical and electronic construction can be simplified. In particular,in an articulated arm, a plurality or else each of the connectionarrangements between the arm members can be embodied with in each casetwo rotary encoders arranged on a common axis of rotation, such thatbesides the relative position of the connection element with respect toits receptacle, it is possible in each case also to determinedeformations as deviation from the desired form, i.e. both deformationsand scale changes, such as e.g. increase or decrease of length ordiameter. Consequently, it is also possible to determine the relativespatial position of all components with respect to one anotherexclusively by means of rotary encoders, wherein further sensors cansupplementarily be used, which, however, do not directly measure thespatial position but rather provide additional parameters, such astemperature sensors, for example, which allow a conclusion to be drawnabout the temperature-governed deformation of the components.

FIG. 9 illustrates an example of a code projection onto a sensorarrangement composed of three sensor lines 15 a-c offset by 60°, saidprojection being produced by a code carrier as code carrier havingpattern elements 14 arranged in a circumferential direction. Byresolving positions of the projected pattern elements 14 on the sensorlines 15 a-c, it is possible, in a manner known per se, to determineboth the rotational angle position and the already explained furtherchanges in position of the code carrier relative to the sensorarrangement thus of the connection element with respect to thereceptacle.

The pattern of the code carrier, which pattern is embodied as a barpattern, for example, has a multiplicity of pattern elements 14 arrangedaround a pattern center one behind another in the direction of rotationat the same distance with respect to one another, said pattern elementsbeing embodied e.g. as light-opaque bars oriented radially. By means ofbeams passing through between the bars, a portion of the bar pattern isimaged as bright and dark regions on the light-sensitive detectorelements.

Moreover, the outwardly and the inwardly directed end sides of the barsform two concentric, discontinuous circle lines that embody patternswhich are symmetrical with respect to the pattern center. By means ofthe sensor lines 15 a-c as detector elements, it is possible here, inparticular during a rotation of the bar pattern, to resolve the lengthsL1 and L2 of the entrances and exits of the respective bars into and outof the spatially resolving region. With the positions resolved in thisway, for example a radial displacement and/or a tilting can then bedetermined computationally. In principle, the position value can bedetermined computationally on the basis of a position of at least one ofthe pattern elements 14, a ratio of positions of a plurality of thepattern elements 14 with respect to one another, or a sequence ofpositions of a plurality of pattern elements 14 arranged one behindanother. In this case, the code or the code projection onto the sensorarrangement can also be designed in a redundant manner, i.e. asoverdetermined with regard to the variable to be determined, such thatthe additional information available as a result of the redundancy canbe used.

FIG. 10 shows an exemplary embodiment which differs from the exemplaryembodiment shown in FIG. 9 by virtue of two sensor lines 5 d and 5 eoffset by 90° as a sensor arrangement and by virtue of a differentembodiment of the pattern, in particular of the pattern elements 14′oriented radially toward the pattern center and arranged one behindanother in the direction of rotation. The code carrier is embodied hereby a light-transmissive glass disk with light-opaque triangles. However,the code carrier rotatable about the axis could also be embodied, forexample, in the form of a thin metal disk having in this case triangularcutouts that embody the pattern elements 14′ arranged one behind anotherin the direction of rotation.

The—for example triangular—embodiment of the pattern elements 14′,wherein mutually facing side lines of adjacent pattern elements 14′arranged one behind another are embodied in a manner essentiallyinclined with respect to the radial direction, has, as a result of theadditional inclination with respect to the radial direction, a greatersensitivity with regard to determining displacements or tilting of thecode carrier by means of the spatially resolving region. It even makesit possible to determine such changes in position of the code carrier bymeans of resolving the width of a single triangle, which is representedhere for the two widths 16 and 17 of the region projected onto thesensor line 15 d. Thus, by way of example, from the width 16 of theprojection, the position or the displacement thereof in here a radialdirection can be identified and its extent can be determined. It goeswithout saying that it is also possible to determine such changes inposition by means of the distances between the triangles. As a resulthere of the triangular form of the pattern elements directed in thedirection of the pattern center, it is possible here by contrast—incomparison with rectangular pattern elements—to provide fewer patternelements arranged one behind another, as a result of which a smallerresolution can be obtained.

However, the sensor arrangement of the rotary encoder can have, inprinciple and in a manner dependent on code configuration and accuracyrequirements, either one or else two or more read heads or sensor lines,wherein, in principle, besides sensor lines as linear arrays, it is alsopossible to use area sensors, i.e. two-dimensional arrangements of pixelsensors. In the case of two or more read heads, the latter can bearranged e.g. in a manner offset with respect to one another 180° in acircumferential direction, wherein said read heads, in the case of fourthereof, can be arranged in a manner offset by 90° in each case in acircumferential direction. In the case of three read heads has, thelatter can be arranged in a manner offset by 120° in each case. Besidesdividing the arrangement with identical angular separations between theread heads or sensor components, however, it is possible to realizesensor arrangements of the rotary encoder having at least four readheads, for example, which are arranged in a manner offset with respectto one another at different angles in a circumferential direction, suchthat e.g. all angular separations differ from one another, in particularare in no ratio of multiples with respect to one another.

Likewise, it is also possible to use for example a, in particular asingle, area sensor, which is arranged on the axis of rotation ordetects the latter and an adjacent region and thus covers a largeangular range in the region in proximity to the axis or else the fullangular range. In particular, in the case of a code carrier, codepatterns can also be fitted on two opposite end faces, said codepatterns in turn being respectively assigned an area sensor covering theaxis of rotation. Such arrangements comprising areal codes that aredetected by a corresponding sensor are known from WO 2008/019855, forexample.

It goes without saying that these illustrated figures merelyschematically illustrate examples of possible embodiments.

What is claimed is:
 1. A surface-surveying measuring machine fordetermining a measurement position, comprising a base, a measurementcomponent for producing and maintaining a contact-making or contactlessmeasurement connection to a surface to be measured, a connectionarrangement comprising at least one connection element which connectsthe measurement component indirectly or directly to the base and atleast one rotary encoder which detects a rotation of the at least oneconnection element with respect to a receptacle, the rotary encoderhaving a code carrier and a sensor arrangement, wherein code carrier andsensor arrangement are rotatable with respect to one another about adefined axis of rotation as a first degree of freedom, wherein, in amanner effected from a code projection being dependent on thethree-dimensional position of the code carrier, a rotational positionrelative to the defined axis of rotation of the code carrier can bedetermined and, on the basis of the code projection, at least oneposition value with regard to at least one of five further degrees offreedom of the three-dimensional position of the code carrier relativeto the sensor arrangement can be determined and provided, an evaluationunit being designed to calculate the current measurement position of themeasurement component with respect to the base whereby the at least oneprovided position value is used as a further current measurementposition variable in addition to the rotational position.
 2. Thesurface-surveying measuring machine as claimed in claim 1, wherein: theat least one provided position value is directly used as further currentmeasurement position variable.
 3. The surface-surveying measuringmachine as claimed in claim 1, wherein: the evaluation unit is designedto link with one another connection element position measurementvariables detected by individual connection element position measuringdevices including the at least one provided position value with respectto the at least one rotary encoder and derive the measurement positionof the measurement component therefrom.
 4. The surface-surveyingmeasuring machine as claimed in claim 1, wherein: the provided positionvalues are a radial displacement direction and a radial displacementextent, an axial displacement extent and a tilting direction and atilting angle.
 5. The surface-surveying measuring machine as claimed inclaim 1, wherein: the evaluation unit is designed to use the at least onposition value to determine a relative position, corresponding to the atleast one further degree of freedom of the code carrier, of the at leastone connection element with respect to the receptacle and/or adeformation of the at least one connection element as a change in shapeand/or size.
 6. The surface-surveying measuring machine as claimed inclaim 1, wherein: the calculation of the measurement position is basedon a model with geometrical and material-dependent variables of theconnection element and/or on a calibration whereby known positions andorientations are assigned corresponding position values.
 7. Thesurface-surveying measuring machine as claimed in claim 6, wherein: incase of a model, at least one variable determined by an additionalsensor, such as a temperature sensor, are supplementarily used in themodel.
 8. The surface-surveying measuring machine as claimed in claim 1,wherein: the further measurement position variable comprises a flexureof the at least one connection element being determined depending on atilting of the code carrier with respect to the axis of rotation.
 9. Thesurface-surveying measuring machine as claimed in claim 1, wherein: themeasurement position is determined exclusively on the basis of therotational position and at least one position value of the rotaryencoder of the at least one connection element and/or the measuringmachine comprises the at least one rotary encoder as single type ofsensor exclusively used for determining the measurement position. 10.The surface-surveying measuring machine as claimed in claim 1, wherein:the machine is embodied as an articulated arm for determining ameasurement position, wherein the articulated arm has a first end asbase, a second end having the measurement component for producing andmaintaining a contact-connecting or contactless measurement connectionto the surface to be measured, and at least two arm elements asconnection elements.
 11. A connection arrangement for asurface-surveying measuring machine, comprising: a connection elementfor indirectly or directly connecting a base to a measurement componentfor producing and maintaining a measurement connection to a surface tobe measured, and at least one rotary encoder designed to detect therotation of the at least one connection element with respect to areceptacle and in each case has a code carrier and a sensor arrangement,wherein code carrier and sensor arrangement are rotatable with respectto one another about a defined axis of rotation as a first degree offreedom, wherein: the rotary encoder is designed for determining, in amanner effected from the code projection being dependent on thethree-dimensional position of the code carrier, a rotational position ofthe code carrier about the axis of rotation and at least one positionvalue with regard to at least one of five further degrees of freedom ofthe three-dimensional position of the code carrier relative to thesensor arrangement, such that the rotary encoder is usable as a rotationangle measuring device and additionally as a measuring device formeasuring of axial and/or radial displacements and/or tilting of thecode carrier.
 12. The connection arrangement as claimed in claim 11,wherein: the at least one position value relates at least to the twofurther degrees of freedom of a deflection of the code carrier from arest position in a radial direction relative to the axis of rotation.13. The connection arrangement as claimed in claim 11, wherein: an exactthree-dimensional position of the code carrier with respect to thesensor arrangement is detected on the basis of the following measurementposition variables: an angle of rotation about the axis of rotation, aradial displacement direction, a radial displacement extent, an axialdisplacement extent, a tilting direction and/or a tilting angle.
 14. Theconnection arrangement as claimed in claim 11, wherein: the positionvalue for the at least one further degree of freedom is used todetermine therefrom a position and/or orientation of the connectionelement and/or a deformation of the connection element, wherein positionand/or orientation of the connection element correspond to the at leastone further degree of freedom of the code carrier.
 15. The connectionarrangement as claimed in claim 11, wherein: the connection arrangementis embodied as a rotary articulated joint having two of said rotaryencoders.
 16. A connection arrangement for a surface-surveying measuringmachine, comprising: a connection element for indirectly or directlyconnecting a base to a measurement component for producing andmaintaining a measurement connection to a surface to be measured, and atleast one rotary encoder designed to detect the rotation of the at leastone connection element with respect to a receptacle and in each case hasa code carrier and a sensor arrangement, wherein code carrier and sensorarrangement are rotatable with respect to one another about a definedaxis of rotation as a first degree of freedom, wherein: the rotaryencoder is designed for explicitly determining, in a manner effectedfrom the code projection being dependent on the three-dimensionalposition of the code carrier, and providing at least one position valuewith regard to at least one of five further degrees of freedom of thethree-dimensional position of the code carrier relative to the sensorarrangement, namely: a deflection of the code carrier in a radialdirection relative to the axis of rotation, and/or a deflection of thecode carrier in the direction of the axis of rotation, and/or a tiltingof the code carrier with respect to the axis of rotation, an evaluationunit designed to use the position value to determine a relativeposition, corresponding to the further degree of freedom of the codecarrier, of the connecting element relative to a holder and/or adeformation of the connecting element as a shape or size change.
 17. Theconnection arrangement as claimed in claim 16, wherein: the relativeposition and/or deformation are quantitatively determined.
 18. Theconnection arrangement as claimed in claim 16, wherein: the evaluationunit is designed to relate changes in position of the code carrier whichgo beyond its rotation to the relative position and/or the deformationof the connection element.
 19. The connection arrangement as claimed inclaim 16, wherein: the evaluation unit is designed to effect a divisioninto deformation- and relative attitude-related components on the basisof the orientation of a further connecting element connected to theholder for the at least one encoder.
 20. The connection arrangement asclaimed in claim 16, wherein: the rotary encoder has at least two codecarriers which are arranged a distance apart and rotatable about thesame axis of rotation and a respective at least one position value isdetermined for each of the code carriers on the basis of the respectivecode projection, and the evaluation unit is designed to determine therelative position of the connecting element relative to the holderand/or the deformation of the connecting element from the linkage of theposition values of the two code carriers.
 21. The connection arrangementas claimed in claim 16, wherein: rotational position, deflection andtilting and thus the position of the code carrier relative to the sensorarrangement in six degrees of freedom are determined for the at leastone rotary encoder.
 22. The surface-surveying measuring machine asclaimed in claim 1, wherein: the sensor arrangement of the rotaryencoder has at least four read heads arranged in a manner offset atdifferent angles with respect to one another in a circumferentialdirection.